Mathematics

• Cauchy–Riemann equations
• Chapman–Kolmogorov equation
• Clairaut's equation
• Fredholm integral equation
  Fredholm integral equation
  In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm.-Equation of the first kind :...
  
  
• Hill differential equation
• Ishimori equation
  Ishimori equation
  The Ishimori equation is a partial differential equation proposed by the Japanese mathematician . Its interest is as the first example of a nonlinear spin-one field model in the plane that is integrable .-Equation:The IE has the form...
  
  
• Laplace's equation
  Laplace's equation
  In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as:where ∆ = ∇² is the Laplace operator and \varphi is a scalar function...
  
  
• Maurer-Cartan equation
• Pell's equation
  Pell's equation
  Pell's equation is any Diophantine equation of the formx^2-ny^2=1\,where n is a nonsquare integer. The word Diophantine means that integer values of x and y are sought. Trivially, x = 1 and y = 0 always solve this equation...
  
  
• Poisson's equation
  Poisson's equation
  In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in electrostatics, mechanical engineering and theoretical physics...
  
  
• Riccati equation
  Riccati equation
  In mathematics, a Riccati equation is any ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form y' = q_0 + q_1 \, y + q_2 \, y^2...
  
  
• Sine-Gordon equation
  Sine-Gordon equation
  The sine–Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. It was originally considered in the nineteenth century in the course of study of surfaces of constant negative...
  
  
• Verhulst equation

Physics

• Ampère's circuital law
• Bernoulli's equation
• Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations
  BBGKY hierarchy
  In statistical physics, the BBGKY hierarchy is a set of equations describing the dynamics of a system of a large number of interacting particles...
  
  
• Boltzmann equation
  Boltzmann equation
  The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
  
  
• Borda–Carnot equation
  Borda–Carnot equation
  In fluid dynamics the Borda–Carnot equation is an empirical description of the mechanical energy losses of the fluid due to a flow expansion. It describes how the total head reduces due to the losses. This in contrast with Bernoulli's principle for dissipationless flow , where the total head is a...
  
  
• Darcy–Weisbach equation
• Dirac equation
  Dirac equation
  The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
  
  
  • Dirac equation in the algebra of physical space
    Dirac equation in the algebra of physical space
    The Dirac equation, as the relativistic equation that describesspin 1/2 particles in quantum mechanics can be written in terms of the Algebra of physical space , which is a case of a Clifford algebra or geometric algebrathat is based in the use of paravectors....
    
    
• Doppler equations
• Drake equation
  Drake equation
  The Drake equation is an equation used to estimate the number of detectable extraterrestrial civilizations in the Milky Way galaxy. It is used in the fields of exobiology and the Search for ExtraTerrestrial Intelligence...
  
   (aka Green Bank equation)
• Einstein's field equation
• Einstein-Maxwell-Dirac equations
  Einstein-Maxwell-Dirac equations
  Einstein-Maxwell-Dirac equations are related to quantum field theory. The current Big Bang Model is a quantum field theory in a curved spacetime. Unfortunately, no such theory is mathematically well-defined; in spite of this, theoreticians claim to extract information from this hypothetical theory...
  
  
• Euler equations (fluid dynamics)
• Euler's equations (rigid body dynamics)
• Relativistic Euler equations
  Relativistic Euler equations
  In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity....
  
  
• Euler–Lagrange equation
• Faraday's law of induction
  Faraday's law of induction
  Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...
  
  
• Fokker–Planck equation
• Fresnel equations
  Fresnel equations
  The Fresnel equations , deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...
  
  
• Friedmann equations
  Friedmann equations
  The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity...
  
  
• Gauss's law for electricity
  Gauss's law
  In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:...
  
  
• Gauss's law for gravity
• Gauss's law for magnetism
• Gibbs–Helmholtz equation
• Gross–Pitaevskii equation
• Hamilton–Jacobi–Bellman equation
• Helmholtz equation
  Helmholtz equation
  The Helmholtz equation, named for Hermann von Helmholtz, is the elliptic partial differential equation\nabla^2 A + k^2 A = 0where ∇2 is the Laplacian, k is the wavenumber, and A is the amplitude.-Motivation and uses:...
  
  
• Karplus equation
  Karplus equation
  The Karplus equation, named after Martin Karplus, describes the correlation between 3J-coupling constants and dihedral torsion angles in nuclear magnetic resonance spectroscopy:J = A \cos^2 \phi + B \cos\,\phi + C...
  
  
• Kepler's equation
  Kepler's equation
  Kepler's equation is M = E -\epsilon \cdot \sin E ,where M is the mean anomaly, E is the eccentric anomaly, and \displaystyle \epsilon is the eccentricity....
  
  
• Kepler's laws of planetary motion
  Kepler's laws of planetary motion
  In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
  
  
• Kirchhoff's diffraction formula
  Kirchhoff's diffraction formula
  Kirchhoff's diffraction formula can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave disturbance when a monochromatic spherical wave passes through an opening in an opaque screen...
  
  
• Klein–Gordon equation
• Korteweg–de Vries equation
  Korteweg–de Vries equation
  In mathematics, the Korteweg–de Vries equation is a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non-linear partial differential equation whose solutions can be exactly and precisely specified...
  
  
• Landau–Lifshitz equation
  Landau–Lifshitz equation
  In physics, the Landau–Lifshitz equation , named for Lev Landau and Evgeny Lifshitz, is a name used for several different differential equations*For the Landau–Lifshitz aeroacoustic equation see aeroacoustics....
  
  
• Lane–Emden equation
• Langevin equation
  Langevin equation
  In statistical physics, a Langevin equation is a stochastic differential equation describing the time evolution of a subset of the degrees of freedom. These degrees of freedom typically are collective variables changing only slowly in comparison to the other variables of the system...
  
  
• Levy–Mises equations
• Lindblad equation
  Lindblad equation
  In quantum mechanics, the Kossakowski–Lindblad equation or master equation in the Lindblad form is the most general type of markovian and time-homogeneous master equation describing non-unitary evolution of the density matrix \rho that is trace preserving and completely positive for any initial...
  
  
• Lorentz equation
• Maxwell's equations
  Maxwell's equations
  Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
  
  
• Maxwell's relations
• Newton's laws of motion
  Newton's laws of motion
  Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
  
  
• Navier–Stokes equations
• Reynolds-averaged Navier–Stokes equations
• Prandtl–Reuss equations
• Prony equation
  Prony equation
  The Prony equation is a historically important equation in hydraulics, used to calculate the head loss due to friction within a given run of pipe...
  
  
• Rankine–Hugoniot equation
• Roothaan equations
  Roothaan equations
  The Roothaan equations are a representation of the Hartree-Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type. It applies to closed-shell molecules or atoms where all molecular orbitals or atomic orbitals, respectively, are doubly occupied. This is generally...
  
  
• Sackur–Tetrode equation
• Schrödinger equation
  Schrödinger equation
  The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
  
  
• Screened Poisson equation
  Screened Poisson equation
  In Physics, the screened Poisson equation is the following partial differential equation:\left[ \Delta - \lambda^2 \right] u = - f...
  
  
• Schwinger–Dyson equation
• Sellmeier equation
  Sellmeier equation
  The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. The equation is used to determine the dispersion of light in the medium....
  
  
• Stokes–Einstein relation
• Tsiolkovsky rocket equation
  Tsiolkovsky rocket equation
  The Tsiolkovsky rocket equation, or ideal rocket equation is an equation that is useful for considering vehicles that follow the basic principle of a rocket: where a device that can apply acceleration to itself by expelling part of its mass with high speed and moving due to the conservation of...
  
  
• Van der Waals equation
  Van der Waals equation
  The van der Waals equation is an equation of state for a fluid composed of particles that have a non-zero volume and a pairwise attractive inter-particle force It was derived by Johannes Diderik van der Waals in 1873, who received the Nobel prize in 1910 for "his work on the equation of state for...
  
  
• Vlasov equation
  Vlasov equation
  The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction...
  
  
• Wiener equation

Chemistry

• Arrhenius equation
  Arrhenius equation
  The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction. The equation was first proposed by the Dutch chemist J. H. van 't Hoff in 1884; five years later in 1889, the Swedish...
  
  
• Henderson–Hasselbalch equation
• Michaelis–Menten equation
• Nernst equation
  Nernst equation
  In electrochemistry, the Nernst equation is an equation that can be used to determine the equilibrium reduction potential of a half-cell in an electrochemical cell. It can also be used to determine the total voltage for a full electrochemical cell...
  
  

Maths

• Algebraic equation
• Polynomial equations
  • Linear equation
    Linear equation
    A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable....
    
    
  • Quadratic equation
    Quadratic equation
    In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
    
    
  • Cubic equation
  • Biquadratic equation
  • Quartic equation
  • Quintic equation
    Quintic equation
    In mathematics, a quintic function is a function of the formg=ax^5+bx^4+cx^3+dx^2+ex+f,\,where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero...
    
    
  • Sextic equation
    Sextic equation
    In mathematics, a sextic equation is a polynomial equation of degree six. It is of the form:ax^6+bx^5+cx^4+dx^3+ex^2+fx+g=0,\,where a \neq 0....
    
    
• Characteristic equation
  Characteristic equation
  Characteristic equation may refer to:* Characteristic equation , used to solve linear differential equations* Characteristic equation, a characteristic polynomial equation in linear algebra used to find eigenvalues...
  
  
• Class equation
• Comparametric equation
  Comparametric equation
  A comparametric equation is an equation that describes a parametric relationship between a function and a dilated version of the same function, where the equation does not involve the parameter. For example, ƒ = 4ƒ is a comparametric equation, when we define g = f, so that we have g = 4ƒ no longer...
  
  
• Difference equation
• Differential equation
  Differential equation
  A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
  
  
  • Ordinary differential equation
    Ordinary differential equation
    In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
    
    
  • Partial differential equation
    Partial differential equation
    In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
    
    
  • Total differential equation
• Diophantine equation
  Diophantine equation
  In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
  
  
• Equation
  Equation
  An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
  
  
• Modular equation
  Modular equation
  In mathematics, a modular equation is an algebraic equation satisfied by moduli, in the sense of moduli problem. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.The most frequent use of the term...
  
  
• Parametric equation
  Parametric equation
  In mathematics, parametric equation is a method of defining a relation using parameters. A simple kinematic example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion....
  
  
• Replicator equation
  Replicator equation
  In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness landscape...
  
  

Physics

• Advection equation
• Barotropic vorticity equation
  Barotropic vorticity equation
  This Barotropic vorticity equation assumes the atmosphere is nearly barotropic, which means that the direction and speed of the geostrophic wind are independent of height. In other words, no vertical wind shear of the geostrophic wind. It also implies that thickness contours are parallel to...
  
  
• Continuity equation
  Continuity equation
  A continuity equation in physics is a differential equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described...
  
  
• Diffusion equation
• Drag equation
  Drag equation
  In fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid....
  
  
• Equation of motion
  Equation of motion
  Equations of motion are equations that describe the behavior of a system in terms of its motion as a function of time...
  
  
• Equation of state
  Equation of state
  In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...
  
  
• Equation of time
  Equation of time
  The equation of time is the difference between apparent solar time and mean solar time. At any given instant, this difference will be the same for every observer...
  
  
• Heat equation
  Heat equation
  The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time...
  
  
• Ideal gas equation
• Ionic equation
• Mass-energy equivalence equation
  Mass-energy equivalence
  In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...
  
  
• Primitive equations
  Primitive equations
  The primitive equations are a set of nonlinear differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models...
  
  
• Relativistic wave equations
  Relativistic wave equations
  Before the creation of quantum field theory, physicists attempted to formulate versions of the Schrödinger equation which were compatible with special relativity...
  
  
• Vorticity equation
  Vorticity equation
  The vorticity equation is an important prognostic equation in the atmospheric sciences. Vorticity is a vector, therefore, there are three components...
  
  
• Wave equation
  Wave equation
  The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...
  
  

Lists of equations

• Constitutive equation
  Constitutive equation
  In physics, a constitutive equation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external forces...
  
  
• Defining equation (physics)
  Defining equation (physics)
  In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units.-Treatment of vectors:There are many forms of vector notation...
  
  
• Defining equation (physical chemistry)
  Defining equation (physical chemistry)
  In physical chemistry, there are numerous quantities associated with chemical compounds and reactions; notably in terms of amounts of substance, activity or concentration of a substance, and the rate of reaction. This article uses SI units....
  
  
• List of equations in classical mechanics
• List of relativistic equations

• Mathematical descriptions of physical laws
  Mathematical descriptions of physical laws
  Physical laws are often summarized by a single equation, or at least a small set of equations. This article tabulates many of the important bands of physics where such laws occur.-Conservation and continuity:...